The work that has been accomplished is just a favourable outset. The model can be further improved, and more significative and valuable work can be done based on the model. The tasks that could be further performed in the next step are outlined as follow:
1. further study the inhibition function
The interrelations between inhibitors need to be further understood. The acclimation to the higher NH4+ and the threshold can not be reflected by current model.
2. explore the decay of biomass
The real case shows that bacteria have faster decay rates, as after weekend (three days starving) the highest biogas production rates on Monday are much lower than on Friday (the reactors are fed on Monday Wednesday and Friday). However, the model is a bit less sensitive to this, though different decay rates had been tested. This phenomenon should be studied further from the mathematical point of view.
3. simulate the delay phenomenon of biochemical processes
This phenomenon can not be simulated so far, although it is nature behaviour of organisms.
4. simulate more types of reactors
In this work, only CSTR was modelled, more types of reactors should be modelled, e.g.
UASB reactor.
5. simulate more AD treatment processes
The AD treatment is a powerful method to deal with wastes and wastewater. More processes can be modelled, e.g. the ammonia removal in ADP (van Dongen et al. 2001), the sulphate reduction in ADP (Ristow and Hansford 2001), etc.
References
Angelidaki, I., Ellegaard, L. and Ahring, B.K., 1993. A mathematical model for dynamic simulation of anaerobic digestion of complex substrates: Focusing on ammonia inhibition. Biotech. Bioeng. Vol 42: 159-166 Barker, H.A., 1956. Biological Formation of Methane. In: Bacterial Fermenttions. John Wiley & Sons, Inc., New
York, U.S.
Batstone, D.J., Keller, J., Angelidaki, I.., Kalyuzhnyi, S., Pavlostathis, S.G., Rozzi, A.., Sanders, W., Siegrist, H.
and Vavilin, V. (IWA Task Group for Mathematical Modelling of Anaerobic Digestion Processes), 2002.
Anaerobic Digestion Model No. 1 (ADM1). IWA Publishing, London, U.K.
Batstone, D.J. and Keller, J., 2003. Industrial applications of the IWA anaerobic digestion model No. 1 (ADM1).
Wat. Sci. Tech. Vol 47, No 12: 199-206
Batstone, D.J., Pind, P.F. and Angelidaki, I., 2003. Kinetics of thermophilic, anaerobic oxidation of straight and branched chain butyrate and valerate. Biotech. Bioeng. Vol 84, No 2: 195-204
Brühl, A.S., 1991. Anaerobe Abwasserreinigung in neuen Bioreaktoren mit Polyurethan-Schaumstoffpartikeln zur Immobilisierung der Bakterien. VDI Verlage GmbH, Düsseldorf. Fortschrittberichte, Reihe 15, Nr. 85:
Umwelttechnik. in German
Chen, Y.R. and Hashimoto, A.G., 1980. Substrate utilization kinetic model for biological treatment process.
Biotech. Bioeng. Vol 22, No 10: 2081-2095
Eastman, J.A. and Ferguson, J.F., 1981. Solubilization of particulate organic carbon during the acid phase of anaerobic digestion. J. Wat. Poll. Cont. Fed. Vol 53: 352-266
Gavala H.N., Angelidaki, I., Ahring, B.K., 2003. Kinetics and Modeling of anaerobic digestion process. Adv.
Biochem. Eng. Biotechnol. Vol 81: 57-93
Gossett, J.M. and Belser, R.L., 1982. Anaerobic digestion of waste activated sludge, J. Environ. Eng. ASCE Vol 108: 1101-1120
Haldane, J.B.S., 1930. Enzymes. Longman Green and Co., London, U.K.
Henze, M., Gujer, W., Mino, T. and van Loosdrecht, M., (IWA Task Group on Mathematical Modelling for Design and Operation of Biological Wastewater Treatment), 2000. Activated Sludge Models ASM1, ASM2, ASM2d and ASM3. IWA Publishing, London, U.K.
Hobson, P.N., 1983. The kinetics of anaerobic digestion of farm wastes. J. Chem. Tech. Biotechnol. Vol 33B:
1-20
Ivanova, M., 2003. Untersuchungen zur Vergärung von Schwarzwasser aus Vakuumtoiletten mit zugegebenen Bioabfällen. Master Thesis, Hamburg University of Technology (TUHH), Germany. in German
Jöbses, I.M.L., 1986. Modelling of anaerobic microbial fermentations – the production of alcohols by Zymomonas mobilis and Clostridium beijerinckii. Krips Repro Meppel
Kayhanian, M., 1999. Ammonia inhibition in high solids biogasification: an overview and practical solutions.
Environ. Technol. Vol 20: 355
Koutsoukos, P., Amjad, Z., Tomson, M.B. and Nancollas G.H., 1980. Crystallization of calcium phosphates: a constant composition study. J. Am. Chem. Soc. Vol 27: 1553-1557
Kujawa-Roeleveld, K., Elmitwalli, T., Gaillard, A., van Leeuwen, M. and Zeeman, G., 2003. Co-digestion of concentrated black water and kitchen refuse in an accumulation system within the DESAR (decentralized sanitation and reuse) concept. Wat. Sci. Tech. Vol 48 No 4: 121–128
L. Jean Emmanuel G., N., 2004. Impact of Mixing, Feeding Frequency and High Nitrogen Concentrations on the Anaerobic Digestion of Blackwater. Master Thesis, Hamburg University of Technology (TUHH), Germany Lay, J.J., Li, Y.Y., Noike, T., 1998. The influence of pH and ammonia concentration on the methane production
in high-solids Digestion Processes. Water Environment Research Vol 70:1075-1082
Lehninger, A., Nelson, D. and Cox, M., 1993. Principles of biochemistry. 2nd ed., Worth Publishers, New York, U.S.
Lens, P., Zeeman, G., Lettinga, G., 2001. Decentralised sanitation and reused: Concepts, systems and implementation. IWA publishing, London, U.K.
Lettinga, G., Van Velsen, A.F.M., Hobma, S.W., De Zeeuw, W. and Klapwijk, A., 1980. Use of the upflow sludge blanket reactor concept for biological waste water treatment, especially for anaerobic treatment.
Biotech. Bioeng. Vol 22: 699–734.
Lema, J.M. and Omil, F., 2001. Anaerobic treatment: a key technology for a sustainable management of wastes in Europe. Wat. Sci. Tech. Vol 44, No 8: 133-140
Lide, D., 2001. CRC Handbook of chemistry and physics. 82nd ed. CRC Press, Boca Raton, FL.
Liu, T. and Sung, S., 2002. Ammonia inhibition on thermophilic aceticlastic methanogens. Wat. Sci. Tech. Vol 45 No 10: 113-120
Madigan, M.T., Martinko, J.M., and Parker, J., 2003. Brock biology of microorganisms. Upper Saddle River, NY: Prentice Hall, 10th ed., International Edition
McCarty, P.L, 2001. The development of anaerobic treatment and its future. Wat. Sci. Tech. Vol 44, No 8: 149-156
Merkel, W. and Krauth, K., 1999. Mass transfer of carbon dioxide in anaerobic reactors under dynamic substrate loading conditions Wat. Res. Vo 33, No 9: 2011-2020
Metcalf, L. and Eddy, H.P., 1915. American Sewerage Practice, III. Disposal of Sewage. 1st ed., McGraw-Hill Book Company, Inc., New York, U.S.
Metcalf & Eddy, 2003. Wastewater Engineering: Treatment and Reuse. 4th ed., McGraw-Hill, Inc.
Michaelis, L. and Menten, L., 1913. Die Kinetik der Invertinwirkung. Biochem. Z. Vol 49: 334-369
Mitsdörffer, R., 1991. Charakteristika der zweistufigen thermophilen/mesophilenSchlammfaulung unter Berücksichtigung kinetischer Ansätze; Berichte aus Wassergüte-und Abfallwirtschaft, TU München
Moen, G.M., 2000. A comparison of the performance and kinetics of thermophilic and mesophilic anaerobic digestion. Master of Science Thesis, Dapartment of Civil and Environmental engineering, University of Washington, Seattle, WA.
Mosey, F., 1983. Mathematical modelling of the anaerobic digestion process: regulatory mechanisms for the formation of short chain volatile fatty acids from glucose. Wat. Sci. Tech. Vol 15, No 8/9: 209-232
Musvoto, E.V., Wentzel, M.C., Loewenthal, R.E. and Ekama, G.A., 2000a. Integrated chemical-physical processes modelling – I. Development of a kinetic-based model for mixed weak acid/base systems. Wat.
Res. Vol 34: 1857-1867
Musvoto, E.V., Wentzel, M.C., Loewenthal, R.E. and Ekama, G.A., 2000b. Integrated chemical-physical processes modelling – II. Development of a kinetic-based model for mixed weak acid/base systems. Wat.
Res. Vol 34: 1869-1880
NRC, 1995. The Role of Technology in Environmentally Sustainable Development. National Academy Press, Washington D.C., U.S.
Otterpohl, R., Grottker, M. and Lange, J., 1997. Sustainable water and waste management in urban areas. Wat.
Sci. Tech. Vol 35, No 9: 121-133
Otterpohl, R., Albold, A. and Oldenburg, M., 1999. Source control in urban sanitation and waste management:
ten systems with reuse of resources. Wat. Sci. Tech. Vol 39, No 5: 153-160
Otterpohl, R., 2001. Black, brown, yellow, grey - the new colours of sanitation. Water 21, October, 2001.
Magazine of the International Water Association. IWA Publishing, London, U.K.
Otterpohl, R., Braun, U. and Oldenburg, M., 2002. Innovative Technologies for Decentralised Wastewater Management in Urban and Peri-Urban Areas. Keynote presentation at IWA Small2002, Istanbul, Sept 2002 Ozkan Yucel, U.G. and Gokcay C.F., 2004. Modeling a full-scale anaerobic digester. The 10th World Congress
on Anaerobic Digestion (AD10), proceedings, Montreal, Canada
Pauss, A., Andre, G., Perrier,M., Guiot, S.R., 1990. Liquid-to-Gas Mass Transfer in Anaerobic Processes:
Inevitable Transfer Limitations of Methane and Hydrogen in the Biomethanation Process. Appl. Environ.
Microbiol. Vol 56, No 6: 1636-1644
Pavlostathis, S.G. and Gossett, J.M, 1986. A kinetic Model for anaerobic digestion of biological sludge. Biotech.
Bioeng. Vol 28, No 10: 1519-1530
Pavlostathis, S.G., and Giraldo-Gomez, E., 1991. Kinetic of anaerobic treatment. Wat. Sci.Technol. Vol 24, No 8: 35-59
Peterson, E.E., 1965. Chemical reaction analysis. Prentice-Hall, Englewood Cliffs, NJ, U.S.
Ramsay, I.R., 1997. Modelling and control of high-rate anaerobic wastewater treatment systems. Ph.D. thesis, University of Queensland, Brisbane, Australia
Reichert, P., 1994. Aquasim - a tool for simulation and data-analysis of aquatic systems. Wat. Sci. Tech. Vol 30 No 2: 21-30
Reichert, P. 1998. Aquasim 2.0 – User Manual, computer program for the identification and simulation of aquatic systems. EAWAG: Dübendorf, Switzerland, ISBN 3 906484 16 5
Ristow, N.E. and Hansford, G.S., 2001. Modelling of a falling sludge bed reactor using AQUASIM. Water SA Vol. 27 No. 4: 445-454
Ruiz, G., Rodriguez, J., Roca, E. and Lema, J.M., 2004. Modification of the IWA-ADM1 for application to anaerobic treatment of ethanolic wastewater from wine factories. The 10th World Congress on Anaerobic Digestion (AD10), proceedings, Montreal, Canada
Shang, Y., Johnson, B.R. and Sieger, R., 2004. Application of the IWA Anaerobic Digestion Model (ADM1) for simulating full-scale anaerobic sewage sludge digestion. The 10th World Congress on Anaerobic Digestion (AD10), proceedings, Montreal, Canada
Siegrist, H., Vogt, D., Garcia-Heras, J.L. and Gujer, W., 2002. Mathematical model for meso- and thermophilic anaerobic sewage sludge digestion. Environ. Sci. Technol. Vol 36 Issue 5: 1113-1123
Stronach, S.M., Rudd, T. and Lester, J.N., 1986. Anaerobic Digestion Process in Industrial Wastewater Treatment. Springer-Verlag, Berlin, Heidelberg, Germany
Stryer, L. 1988. Biochemistry. 3rd ed., W. H. Freeman & Co., New York, , U.S.
ten Brummeler, E., Horbach, H.C.J.M. and Koster, I.W., 1991. Dry anaerobic batch digestion of the organic fraction of municipal solid waste. J. Chem. Tech. Biotechnol. Vol 50: 191-209
Torre, A.D., Stephanopoulos, G., 1986. Mixed culture model of anaerobic digestion: Application to the valuation of startup procedures. Biotech. Bioeng. Vol 28: 1106-1118
van Dongen, U., Jetten, M.S.M. and van Loosdrecht, M.C.M., 2001. The SHARON®-Anammox® process for treatment of ammonium rich wastewater. Wat. Sci. Tech. Vol 44, No 1: 153-160
van Lier, J.B., Rebac, S. and Lettinga, G., 1997. High-rate anaerobic wastewater treatment under psychrophilic and thermophilic conditions. Wat. Sci. Tech. Vol 35, No 10: 199-206
van Velsen, A.F.M., 1977. Anaerobic digestion of piggery waste. Netherlands Journal of Agricultural Science Vol 25: 151
Vavilin, V.A., Rytov, S.V. and Lokshina, L.Y., 1996. A description of hydrolysis kinetics in anaerobic degradation of particulate organic matter. Biores. Tech. Vol 56: 229-237
Veeken, A. and Hamelers, B., 1999.Effect of temperature on hydrolysis rates of selected biowaste components.
Biores. Technol. Vol 69, No 3: 249-254
Veeken, A., Kalyuzhyi, S., Scharff, H. and Hamelers, B., 2000. Effect of pH and VFA on hydrolysis of organic solid waste. J. Environ. Eng. Vol 126, No 12: 1076-1081
Wendland, C., Deegener, S., Behrendt, J. and Otterpohl, R., 2004. Anaerobic digestion of blackwater from vacuum toilets. The 10th World Congress on Anaerobic Digestion (AD10), proceedings, Montreal, Canada Whitman, W.G., 1923. The two-film-theory of absorption. Chem. Met. Eng. Vol 29: 147
Zeeman, G. and Lettinga, G., 1999. The role of anaerobic digestion of domestic sewage in closing the water and nutrient cycle at community level. Wat. Sci. Tech. Vol 39, No 5: 187-194
Appendix
Appendix A : The list of symbols and abbreviations
Abbreviation Description Abbreviation Description
AA amino acids HVa valeric acid
Ac- acetate IC Inorganic Carbon
AD anaerobic digestion IN Inorganic Nitrogen
ADP anaerobic digestion process LCFA long chain fatty acids BPR biogas production rate MS monosaccharides
Bu- butyrate NH3-N ammonia nitrogen
BWAD blackwater anaerobic digestion NH4-N ammonium nitrogen
CH4 methane Pr- propionate
CO2 carbon dioxide SCFA short chain fatty acids COD Chemical Oxygen Demand Sec. section
CSTR Continual Stirred Tank Reactor SI soluble inerts DAE Differential-Algebraic Equation SRT sludge retention time DE Differential Equation TAN total ammonium nitrogen DESAR decentralized sanitation and reuse TC Total Carbon
ECOSAN ecological sanitation TIC Total Inorganic Carbon
Eqn. equation TIN Total Inorganic Nitrogen
F1 KR feed once per week TN Total Nitrogen F2 KR feed once per two weeks TOC Total Organic Carbon FAN free ammonia nitrogen TSS Total Suspended Solids
F/M Food biomass ratio TUHH Hamburg University of Technology GC gas chromatography Va- valerate
HAc acetic acid VFA Volatile fatty acids
HBu butyric acid VS Volatile Solids
HPr Propionic acid WWTP wastewater treatment plants HRT hydraulic retention time XI particulate inerts
* The mathematical symbols and their units can be found in Table 1, on page 8.
Appendix B : The matrix of biochemical processes (modified from ADM1)
Component i → 1 2 3 4 5 6 7 8 9 10 11 12
j Process j ↓ Ssu Saa Sfa Sva Sbu Spro Sac Sh2 Sch4 SIC SIN SI Reaction rate: ρj, g COD/(m3·d)
Ci C content Csu Caa Cfa Cva Cbu Cpro Cac Cch4 CIC CSI
Ni N content Naa CIN NSI
0 raw Xc,raw fva_xc,raw fbu_xc,raw fpro_xc,raw fac_xc,raw
1 Disintegration ∑
2 Hydrolysis Carbohydrates 1.0 ∑
=1~9,11~24
Mono- saccharides (g COD/m3 ) Amino acids (g COD/m3) LCFA (g COD/m3) Total valerate (g COD/m3) Total butyrate (g COD/m3) Total propionate (g COD/m3) Total acetate (g COD/m3 ) Hydrogen gas (g COD/m3 ) Methane gas (g COD/m3) Inorganic carbon (mole C/m3) Inorganic nitrogen (g N/m3) Soluble inerts (g COD/m3 ) Inhibition factors:
I1 = IpH·IIN,lim
I2 = IpH·IIN,lim·Ih2
I3 = IpH·IIN,lim·INH3,ac
The matrix of biochemical processes (Continued)
Composites (g COD/m3) Carbohydrates (g COD/m3 ) Proteins (g COD/m3) Lipids (g COD/m3) Sugar degraders (g COD/m3) Amino acid degraders (g COD/m3) LCFA degraders (g COD/m3) Valerate and butyrate degraders (g COD/m3) Propionate degraders (g COD/m3) Acetate degraders (g COD/m3) Hydrogen degraders (g COD/m3) Particulate inerts (g COD/m3) Raw input (g COD/m3) Inhibition factors:
I1 = IpH·IIN,lim
I2 = IpH·IIN,lim·Ih2
I3 = IpH·IIN,lim·INH3,ac
Appendix C : The DE implementation for acid-base processes Acid-base processes are implemented as dynamic processes
Component i → 4a 4b 5a 5b 6a 6b 7a 7b 10a 10b 10c 11a 11b
j Process j ↓ SHVa SVa- SHBu SBu- SHPro SPro- SHAc SAc- SCO2 SHCO3- SCO3-- SNH4+ SNH3 Reaction rate: ρj, g COD/(m3·d)
AB-1 Valerate 1 -1
kA/B,HVa
(
SVa- ⋅SH+ −Ka,va⋅SHVa)
AB-2 Butyrate 1 -1 kA/B,HBu
(
SBu- ⋅SH+ −Ka,bu⋅SHBu)
AB-3 Propionate 1 -1
kA/B,HPro
(
SPro- ⋅SH+ −Ka,pro⋅SHPro)
AB-4 Acetate 1 -1
kA/B,HAc
(
SAc- ⋅SH+ −Ka,ac⋅SHAc)
AB-5 Carbon dioxide 1 -1
(
- 2 2 3)
2 HCO3 H a,CO HCO
CO
A/B, S S K S
k ⋅ + − ⋅
AB-5 Bicarbonate 1 -1
kA/B,HCO3-
(
SCO23-⋅SH+ −Ka,HCO-3⋅SHCO-3)
AB-7 Ammonium 1 -1
kA/B,NH+4
(
SNH3⋅SH+ −Ka,NH+4 ⋅SNH+4)
Valeric acid (g COD/m3 ) Valerate (g COD/m3 ) Butyric acid (g COD/m3 ) Butyrate (g COD/m3 ) Propionic acid (g COD/m3 ) Propionate (g COD/m3 ) Acetic acid (g COD/m3 ) Acetate (g COD/m3 ) Carbon-dioxide (mole C/m3 ) Bicarbonate (mole C/m3 ) Carbonate (mole C/m3 ) Ammonium (g N/m3 ) Ammonia (g N/m3 ) * kA/B,i (m3·mole-1·d-1) can be in between 107
and 1014, and generally the same results will be attained.
** For each acid-base this process can not be implemented together with its process in Append E
Appendix D : The DAE implementation for acid-base processes Acid-base processes are implemented as equilibrium processes
Equation Variable
Appendix E : The values of biochemical processes parameters 1. Carbon content (Ci) and Nitrogen content (Ni) of each component
j Name Description C content mole C/g COD N content g N/g COD Remark
1 Ssu monosaccharides Csu 6/192 Nsu 0
2 Saa amino acids Caa 0.0300 Naa 0.098
3 Sfa total LCFA Cfa 0.0217 Nfa 0
4 Sva total valerate Cva 5/208 Nva 0
5 Sbu total butyrate Cbu 4/160 Nbu 0
6 Spro total propionate Cpro 3/112 Npro 0
7 Sac total acetate Cac 2/64 Nac 0
8 Sh2 hydrogen Ch2 0 Nh2 0
9 Sch4 methane Cch4 1/64 Nch4 0
10 SIC inorganic carbon CIC - NIC 0
11 SIN inorganic nitrogen CIN 0 NIN 1
12 SI soluble inerts CSI 0.0300 NSI 0.028
13 Xc composite CXc 0.0279 NXc 0.028
14 Xch carbohydrates Cch 0.0313 Nch 0
15 Xpr proteins Cpr 0.0300 Npr 0.098
16 Xli lipids Cli 0.0217 Nli 0
17~23 Xsu~h2 biomass Cbiom 5/160 Nbiom 0.0875 biomass 24 XI particulate inerts CXI 0.0300 NXI 0.028
0 Xc,raw raw input CXc,raw 0.0217 NXc,raw 0.028
* The values partly come from ADM1, and partly come from Mr. Batstone by personal contact.
** The number in the first column is the number of processes in Appendix B. The following tables have the same arrangement.
*** Normally IC refers CO2 and its derivatives, which have 0 g COD content, so the carbon content coefficient of IC is not given here. It is also unnecessary.
2. The values of stoichiometric parameters for mass flux
No Name Description ADM1 Without va
Without
va & bu Remark fsI_xc soluble inert from composites 0.1 0.1 0.1 1-fch_xc-fli_xc-fpr_xc-fxI_xc
fxI_xc particulate inert from composites 0.25 0.25 0.25
fch_xc carbohydrates from composites 0.2 0.2 0.2
fpr_xc proteins from composites 0.2 0.2 0.2
fli_xc lipids form composites 0.25 0.25 0.25
fsu_li sugars from lipids 0.05 0.05 0.05 1-ffa_li
ffa_li LCFA from lipids 0.95 0.95 0.95
fh2_su hydrogen from sugars 0.1906 0.1906 0.2172 0.33*η1,su+0.17*η3,su
fbu_su butyrate from sugars 0.1328 0.1328 - 0.83*η3,su
fpro_su propionate from sugars 0.2690 0.2690 0.2690 0.78*η2,su
fac_su acetate from sugars 0.4076 0.4076 0.5138 0.67*η1,su+0.22*η2,su
fh2_aa hydrogen from amino acids 0.06 0.08 0.1465 1-fva_aa-fbu_aa-fpro_aa-fac_aa
fva_aa valerate from amino acids 0.23 - -
fbu_aa butyrate from amino acids 0.26 0.26 -
fpro_aa propionate from amino acids 0.05 0.1742 0.1742
fac_aa acetate from amino acids 0.4 0.4858 0.6793
η1,su sugar gradation coefficient 1 0.495 0.495 - 1- η2,su – η3,su η2,su sugar gradation coefficient 2 0.345 0.345 -
η3,su sugar gradation coefficient 3 0.16 0.16 -
fxc_xc,raw from raw blackwater to XC 0.72 0.73 0.74
fva_xc,raw valerate in raw blackwater 0.01 0 0
fbu_xc,raw butyrate in raw blackwater 0.02 0.02 0
fpro_xc,raw propionate in raw blackwater 0.05 0.05 0.06
fac_xc,raw acetate in raw blackwater 0.20 0.20 0.20
* The data partly come from ADM1, and partly come from Mr. Batstone by personal contact.
** Other fixed coefficients can be found directly from Peterson Matrix in Appendix B.
*** The coefficients for cases of “without va” and “without va & bu” are figured out based on the values from ADM1.
**** The raw blackwater (XC,raw) is first distributed to composites (XC) and SCFA, as it contains quite a few amount of SCFA.
3. The values of biochemical kinetics parameters
j Name Description ADM1 Used Min Max. Unit disintegration and hydrolysis rates
1 kdis disintegration rate of composites 0.5 4.5 0.013 0.700 d-1
2 khyd_ch hydrolysis rate of carbohydrates 10 10 d-1
3 khyd_pr hydrolysis rate of proteins 10 10 d-1
4 khyd_li hydrolysis rate of lipids 10 10 d-1
biomass decay
13 kS_su sugar degraders 0.02 0.03 0.010 0.800 d-1
14 kdec_aa amino acid degraders 0.02 0.03 0.010 0.800 d-1
15 kdec_fa LCFA degraders 0.02 0.02 0.010 0.060 d-1
16 kdec_c4 valerate and butyrate degraders 0.02 0.03 0.010 0.030 d-1
17 kdec_pro propionate degraders 0.02 0.04 0.010 0.060 d-1
18 kdec_ac acetate degraders 0.02 0.04 0.010 0.050 d-1
19 kdec_H2 hydrogen degraders 0.02 0.04 0.009 0.300 d-1
Maximum uptake rate
5 km_su sugar degraders 30 30 27.0 5067.0 d-1 6 km_aa amino acid degraders 50 50 27.0 53.0 d-1
7 km_fa LCFA degraders 6 6 1.9 363.0 d-1
8~9 km_c4 valerate and butyrate degraders 20 18 5.3 41.0 d-1
10 km_pro propionate degraders 13 14 11.0 23.0 d-1
11 km_ac acetate degraders 8 13 6.4 19.0 d-1 12 km_H2 hydrogen degraders 35 35 25.0 44.0 d-1
half saturation concentration
5 KS_su sugar degraders 500 500 50 1280 g COD/m3 6 KS_aa amino acid degraders 300 300 50 1198 g COD/m3 7 KS_fa LCFA degraders 400 400 100 9210 g COD/m3 8~9 KS_c4 valerate and butyrate degraders 300 110 13 280 g COD/m3
10 KS_pro propionate degraders 300 120 20 373 g COD/m3
11 KS_ac acetate degraders 150 160 40 384 g COD/m3 12 KS_H2 hydrogen degraders 0.007 0.007 0.001 0.6 g COD/m3
11 KS_NH3_all IN limitation to all degraders 1.4 1.4 g N/m3
yield from substrates to degraders
5 Y_su sugar degraders 0.1 0.1 0.07 0.17 COD/COD 6 Y_aa amino acid degraders 0.08 0.08 0.058 0.15 COD/COD 7 Y_fa LCFA degraders 0.06 0.06 0.004 0.055 COD/COD
j Name Description ADM1 Used Min Max. Unit 8~9 Y_c4 valerate and buterate degraders 0.06 0.06 COD/COD 10 Y_pro propionate degraders 0.04 0.04 0.019 0.055 COD/COD 11 Y_ac acetate degraders 0.05 0.05 0.027 0.076 COD/COD 12 Y_h2 hydrogen degraders 0.06 0.06 0.05 0.06 COD/COD
50% inhibitory concentration
7 KI_H2_fa hydrogen to LCFA uptake 0.005 0.005 g COD/m3
8~9 KI_H2_c4 hydrogen to bu and va uptake 0.01 0.01 g COD/m3
10 KI_H2_pro hydrogen to propionate uptake 0.0035 0.0035 g COD/m3
11 KI_NH3_ac Free NH3 to acetate uptake 25.2 200
50 g N/m3 upper and lower pH of 50% inhibitory level
5~10 pH_su~pro_ul 5.5 5.5 -
5~10 pH_su~pro_ll
only lower pH inhibition
considered 4.0 4.0 -
11 pH_ac_ul 8.0 -
11 pH_ac_ll
both lower and upper inhibition
considered 6.0 -
12 pH_h2_ul 6.0 6.0 -
12 pH_h2_ll
only lower pH inhibition
considered 5.0 5.0 -
* The variation range of each parameter is summarized from the literature review of ADM1.
Appendix F : The physicochemical constants 1. Acid-base equilibrium constants
No Acid/base pKa (-) at 298K ΔH0 (j/mole) Ka (mM) at 311K Remark
1 HAc/Ac- 4.76 - 0.017378
2 HBu/Bu- 4.84 - 0.014454
3 CO2/HCO3- 6.35 7,646 0.000508 4 HCO3-/CO32- 10.33 14,850 4.93 x 10-4
5 H2O/(OH-) 14.00 55,900 2.08 x 10-8 Ka =10(-pKa+6)
6 NH3/NH4+ 9.25 51,965 1.11 x 10-6
7 HPr/Pr- 4.88 - 0.013183
8 HVa/Va- 4.80 - 0.015849
* The values of pKa and ΔH0 are gotten from Lide (2001).
** Ka is calculated by Eqn. (21): Ka =10(-pKa+3). Exponent pluses 3 because the unit is transformed from M (≡ kmole/m3) to mM (≡ mole/m3), and H2O needs to plus 6 as both OH -and H+ are involved.
*** When ΔH0 is available, temperature compensation is included by van’t Hoff equation (42).
2. Liquid-gas transfer parameters
No Acid/base K at 298K H (mMliq/bargas) ΔH0 (j/mole) Diffusivity (m2/s x109)
at 311K Remark
1 H2 0.78 -4,180 4.65
2 CH4 1.4 -14,240 1.57
3 CO2 35 -19.410 1.98
4 NH3 57,540
* The values are gotten from Lide (2001).
** Normally NH3 is not calculated in headspace due to its high KH value.
*** When ΔH0 is available, temperature compensation is included by van’t Hoff equation (42).
Appendix G : The specification of the model file
The name of the basic model file is ADM_1_2004-03.31-04.20_refer_ohne_va.aqu
The file is explained in the four parts, i.e. VARIABLE, PROCESS, COMPARTMENT, and LINK, which are the same structure as AQUASIM:
1. VARIABLE
Legend: f_ac_aa
first position second position third position The meaning of the variable in first position:
Symbol Indication Unit Symbol Indication Unit
C_i carbon content of i mole C/ g COD nue_i_su fraction of i from sugars -
COD_S Soluble COD g COD/m3 Patm pressure of atmosphere bar
COD_Tot total COD g COD/m3 Pgas_i partial pressure of gas i bar
COD_X particulate COD g COD m3 Pgas_i_dried partial pressure of gas i (dried) - Exp_i Experimental data of component i - Pgas_tot total gas pressure bar
f_i_j yield of i from j - pH pH -
I_i_j Inhibition of i to j - pKa_i acid equilibrium constant of i at 298K - iniS_i initial condition of i in reactor g COD/m3 probeGas_S_i probe Variable of gas i in headspace g COD/m3 inPercent_xc percentage of Xc in raw input - probeLiq_S_i probe Variable of gas i in reactor g COD/m3
inQ input flow rate m3/d Qgas total gas flow m3/d
inS_i input concentration of i g COD/m3 Qgas_Spec specific norm gas flow m3/m3
kAB_i kinetic constant for acid i m3/(mole·d) Qout effluent m3/d
Ka_i dissociation constant of acid i mole/m3 R gas law constant (mM·K) bar/
kdec_i decay rate of biomass i d-1 S_i concentration of soluble component i g COD/m3
kdis composites disintegration rate d-1 T absolute temperature K
KH_i non-dimensional henry's law
constant mMmMgasliq/ t time d
khyd_i Hydrolysis rate of i d-1 V reactor volume m3
KI_i_j inhibitory concentration of i to j g COD/m3 V_reactor probe Variable of reactor volume m3 kLa liquid-gas transfer coefficient kLa d-1 X_i concentration of particulate i g COD/m3 km_i maximum uptake rate of i d-1 Y_i yield of biomass on uptake of i COD/ COD kp pipe resistance coefficient m3/(bar·d) _inQ_dyn_i coefficient of input (for dynamic input) - Ks_i half saturation constant of substrate i g COD/m3 _inQ_vol_i Input volume of case i m3/batch
M_i Molar weight g/mole _inS_j_i input concen. of j at case i g COD/m3
mue_X_i growth rate of biomass i d-1 _inXc_raw_i The raw input concen. at case i g COD/m3 N_i nitrogen content of i g COD g N/ _Percent_j percentage of j (SCFA) in raw input -
* Normally the unit of S_i and X_i is g COD /m3, but S_i is mole C/m3 and g N/m3 for carbon and nitrogen, respectively.
** The units of experimental data are corresponding to their objects.
The meaning of the variables in second and third positions:
The meaning of the variables in second and third positions: